Bipartite output consensus for heterogeneous linear multi-agent systems with fully distributed protocol

This paper addresses the problem of bipartite output consensus of heterogeneous multi-agent systems over signed graphs. First, under the assumption that the sub-graph describing the communication topology among the agents is connected, a fully distributed protocol is provided to make the heterogeneous agents achieve bipartite output consensus. Then for the case that the topology graph has a directed spanning tree, a novel adaptive consensus protocol is designed, which also avoids using any global information. Each of these two protocols consists of a solution pair of the regulation equation and a homogeneous compensator. Numerical simulations show the effectiveness of the proposed approach.     

Event-triggered control of leader-following and cluster consensus for MAS under directed graph with designable minimum event interval

This paper investigates the event-based consensus problems for linear multi-agent systems under directed network topology. First, a new event-triggered control method is proposed for the leader-following consensus problem of agents under directed graphs. Then this new method is applied to the cluster control problem under special topological conditions. The new event-based control scheme is better than some existing literature in the following aspects. 1) The graph only needs to contain a spanning tree instead of being required to be strongly connected graph or undirected, and the triggering function is state-dependent rather than time-dependent. 2) Some parameters are designable for the trade-off between the event interval and the performance of the controlled system. Besides, the optimization of some parameters is studied to reduce the trigger frequency. All the agents can achieve consensus with an exponential speed when communications among follower agents are intermittent, and Zeno behavior is excluded under the proposed method. 3) When applying this method to the cluster control problem, agents in the same cluster share the same form of triggering function. Cluster consensus can be achieved regardless of intra- and inter-cluster relative coupling strength under the event-triggered control framework.     

Consensus of linear multi-agent systems based on full-order observer

This paper considers distributed consensus problem of multi-agent systems consisting of general linear dynamics with a time-invariant communication topology. A distributed full-order observer type consensus protocol based on relative output measurements of neighbor agents is proposed. It is found that the consensus problem of linear multi-agent systems with a directed communication topology having a spanning tree can be solved if and only if all subsystems are asymptotically stable. Some necessary and sufficient conditions are obtained for ensuring consensus in multi-agent systems. The design technique is based on algebraic graph theory, Riccati inequality and linear control theory. Finally, simulation example is given to illustrate the effectiveness of the theoretical results.     

Scaled consensus of second-order multi-agent systems based on edge-event driven control

In this paper, the scaled consensus of resource-limited multi-agent systems with second-order integrator dynamics and undirected topologies is investigated. In order to reduce bandwidth and computation requirements, a scaled consensus protocol based on periodic edge-event driven control is proposed. It is proven that all the agents could converge to a scaled consensus state while the interaction topology is connected. Moreover, a self-triggered scheme is proposed so as to further reduce communication times between agents. Notably, the event-detecting period is introduced so that Zeno behavior could be excluded in our model. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.     

Couple-group consensus for multi-agent networks of agents with discrete-time second-order dynamics

This paper considers the couple-group consensus problem for multi-agent networks with fixed and directed communication topology, where all agents are described by discrete-time second-order dynamics. Consensus protocol is designed such that some agents in a network reach a consistent value, while other agents reach another consistent value. The convergence of the system matrix is discussed based on the tools from matrix theory. An algebraic condition is established to guarantee couple-group consensus. Moreover, for a given communication topology, a theorem is derived on how to select proper control parameters and sampling period for couple-group consensus to be reached. Finally, simulation examples are presented to validate the effectiveness of the theoretical results.     

Distributed tracking control of second-order multi-agent systems with sampled data

This paper studies the leader–follower consensus problem of second-order multi-agent dynamical systems with fixed and stochastic switching topologies in a sampled-data setting. A distributed linear consensus protocol is designed to track an active leader, where the current position information of neighbor agents and self-velocity data are utilized. A necessary and sufficient condition is established under fixed and directed topology for reaching consensus, which depends on the sampling period and control gain parameters. A sufficient condition is obtained under the Markov switching topology case. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results.     

Designing distributed consensus protocols for second-order nonlinear multi-agents with unknown control directions under directed graphs

This paper focuses on the leaderless and leader-following consensus problems of second-order nonlinear multi-agents under directed graphs. Both leaderless and leader-following consensus protocols are proposed for multi-agents with unknown control directions based on the Nussbaum-type gains. For the leaderless case, the proposed protocol can guarantee that the consensus errors asymptotically converge to zero. Moreover, for the leader-following case, the Lyapunov stability analysis shows that the consensus tracking errors can be made arbitrarily small by tuning the control parameters. It should also be noted that these proposed protocols do not require any information about the global communication topology and work with only the relative information of neighboring agents. Illustrative examples are given to show the effectiveness of the proposed control protocols.     

Robust quantized consensus of discrete multi-agent systems under input saturation

In this paper, we consider the quantized consensus problem of multiple discrete-time integrator agents which suffer from input saturation. As agents transmit state information through communication networks with limited bandwidth, the states of agents have to be quantized into a finite number of bits before transmission. To handle this quantized consensus problem, we introduce an internal time-varying saturation function into the controllers of all agents and ensure that the range of the state of each agent can be known in advance by its neighboring agents. Based on such shared state range information, we construct a quantized consensus protocol which implements a finite-bit quantization strategy to all states of agents and can guarantee the achievement of the asymptotic consensus under any given input saturation threshold. Such desired consensus can be guaranteed at as low bit rate as 1 bit per time step for each agent. Moreover, we can place an upper bound on the convergence rate of the consensus error of agents. We further improve that quantized consensus protocol to a robust version whose parameters are determined with only an upper bound on the number of agents and does not require any more global information of the inter-agent network. Simulations are done to confirm the effectiveness of our quantized consensus protocols.     

Analysis of distributed consensus protocols with multi-equilibria under time-delays

In this paper, we propose a novel method for addressing the multi-equilibria consensus problem for a network of n agents with dynamics evolving in discrete-time. In this method, we introduce, for the first time in the literature, two concepts called primary and secondary layer subgraphs. Then, we present our main results on directed graphs such that multiple consensus equilibria states are achieved, thereby extending the existing single-state consensus convergence results in the literature. Furthermore, we propose an algorithm to determine the number of equilibria for any given directed graph automatically by a computer program. We also analyze the convergence properties of multi-equilibria consensus in directed networks with time-delays under the assumption that all delays are bounded. We show that introducing communication time-delays does not affect the number of equilibria of the given network. Finally, we verify our theoretical results via numerical examples.     

Distributed control of cluster lag consensus for first-order multi-agent systems on QUAD vector fields

This paper addresses the problem of cluster lag consensus for first-order multi-agent systems which can be formulated as moving agents in a capacity-limited network. A distributed control protocol is developed based on local information, and the robustness of the protocol is analyzed by using tools of Frobenius norm, Lyapunov functional and matrix theory. It is shown that when the root agents of the clusters are influenced by the active leader and the intra-coupling among agents is stronger enough, the multi-agent system will reach cluster lag consensus. Moreover, cluster lag consensus for multi-agent systems with a time-varying communication topology and heterogeneous multi-agent systems with a directed topology are studied. Finally, the effectiveness of the proposed protocol is demonstrated by some numerical simulations.     

Distributed consensus of a class of networked heterogeneous multi-agent systems

In this paper, we consider the consensus problem of a class of heterogeneous multi-agent systems composed of the linear first-order and second-order integrator agents together with the nonlinear Euler–Lagrange (EL) agents. First, we propose a distributed consensus protocol under the assumption that the parameters of heterogeneous system are exactly known. Sufficient conditions for consensus are presented and the consensus protocol accounting for actuator saturation is developed. Then, by combining adaptive controller and PD controller together, we design a protocol for the heterogeneous system with unknown parameters (in the nonlinear EL dynamics). Based on graph theory, Lyapunov theory and Barbalat's Lemma, the stability of the controllers is proved. Simulation results are also provided to illustrate the effectiveness of the obtained results.     

A continuous-time consensus algorithm using neurodynamic system for distributed time-varying optimization with inequality constraints

In this paper, a distributed time-varying convex optimization problem with inequality constraints is discussed based on neurodynamic system. The goal is to minimize the sum of agents’ local time-varying objective functions subject to some time-varying inequality constraints, each of which is known only to an individual agent. Here, the optimal solution is time-varying instead of constant. Under an undirected and connected graph, a distributed continuous-time consensus algorithm is designed by using neurodynamic system, signum functions and log-barrier penalty functions. The proposed algorithm can be understood through two parts: one part is used to reach consensus and the other is used to achieve gradient descent to track the optimal solution. Theoretical studies indicate that all agents will achieve consensus and the proposed algorithm can track the optimal solution of the time-varying convex problem. Two numerical examples are provided to validate the theoretical results.     

PI consensus error transformation for adaptive cooperative control of nonlinear multi-agent systems

A solution is provided in this paper for the adaptive approximate consensus problem of nonlinear multi-agent systems with unknown and non-identical control directions assuming an underlying graph topology having a spanning tree. This is achieved with the introduction of a novel variable transformation called PI consensus error transformation. The new variables include the position error of each agent from some reference trajectory chosen by him, which represents the agent’s selection for the desired swarm trajectory, along with an integral term of the weighted total displacement of the agent’s position from all neighbor positions. It is proven that if these new variables are bounded and regulated to zero, then asymptotic approximate consensus among all agents is ensured. Using classical Nussbaum gain based techniques, distributed controllers are designed to regulate the PI consensus error variables to zero and ultimately solve the approximate agreement problem. The proposed approach also allows for a specific calculation of the final consensus trajectory based on the controller parameter selection and the associated graph topology. It is shown that all agent positions converge towards a neighborhood of the weighted average of all agents reference trajectories. Simulation results verify our theoretical derivations.     

Distributed cruise control of high-speed trains

In this work, the cruise control problem of high-speed trains’ movements is investigated. Both cases of a single high-speed train and multiple high-speed trains are under consideration. Different with most existing studies where the centralized control or the decentralized control methods are adopted based on a single point mass model of the train, in this paper, a distributed control mechanism is proposed by virtue of the graph theory, and the high-speed train’s model is built as a cascade of point masses connected by flexible couplers. For a single high-speed train, the neighboring cars interact through the coupling force with each other, which can be described by a connected topological graph by regarding each car as a node. Besides, the speed information communication among the cars is considered to be described by another directed topological graph. A distributed control strategy is then developed, with which all the cars of a train track a desired speed asymptotically and the neighboring cars keep a safety distance from each other. For the multiple high-speed trains running on a railway line, the in-train force interaction topology and the speed information communication topology of all the trains are more complex than those of a single train. A new cluster consensus technique is developed, by which a distributed control law is designed. Under the control law, the trains can track the desired speeds asymptotically, the headway distance between adjacent trains and the distance between the neighboring cars of a train can be kept in appropriate ranges. Finally, simulations are provided to illustrate the effectiveness of the obtained theoretical results.     

Network topology design to influence the effects of manipulative behaviors in a social choice procedure

A social choice procedure is modeled as a Nash game among the social agents. The agents are communicating with each other through a social communication network modeled by an undirected graph and their opinions follow a dynamic rule modelling conformity. The agents’ criteria for this game are describing a trade off between self-consistent and manipulative behaviors. Their best response strategies are resulting in a dynamic rule for their actions. The stability properties of these dynamics are studied. In the case of instability, which arises when the agents are highly manipulative, the stabilization of these dynamics through the design of the network topology is formulated as a constrained integer programming problem. The constraints have the form of a Bilinear Matrix Inequality (BMI), which is known to result in a nonconvex feasible set in the general case. To deal with this problem a Genetic Algorithm, which uses an LMI solver during the selection procedure, is designed. Finally, through simulations we observe that in the case of topologies with few edges, e.g. a star or a ring, the isolation of the manipulative agents is an optimal (or suboptimal) design, while in the case of well-connected topologies the addition or the rewiring of just a few links can diminish the negative effects of manipulative behaviors.     

Matrix-weighted consensus for multi-agent systems with sampled-data

This paper researches the consensus issue for multi-agent systems on matrix-weighted directed fixed and undirected switching network topologies by sampled data control method which saves resources and is more practical. Using the sampled information, the distributed control laws are designed under two network topologies, respectively. Under directed fixed network topology, the consensus conditions based on the sampling period and the eigenvalues of Laplacian matrix are deduced by matrix theory and analysis theory. Under undirected switching network topology, by using Lyapunov stability theory, the consensus conditions based on the sampling period and switched network topologies are built. Lastly, two simulation examples are offered to verify the validity of the obtained results.     

Continuous-time distributed optimization with strictly pseudoconvex objective functions

In this paper, the distributed optimization problem is investigated by employing a continuous-time multi-agent system. The objective of agents is to cooperatively minimize the sum of local objective functions subject to a convex set. Unlike most of the existing works on distributed convex optimization, here we consider the case where the objective function is pseudoconvex. In order to solve this problem, we propose a continuous-time distributed project gradient algorithm. When running the presented algorithm, each agent uses only its own objective function and its own state information and the relative state information between itself and its adjacent agents to update its state value. The communication topology is represented by a time-varying digraph. Under mild assumptions on the graph and the objective function, it shows that the multi-agent system asymptotically reaches consensus and the consensus state is the solution to the optimization problem. Finally, several simulations are carried out to verify the correctness of our theoretical achievements.     

Second-order group consensus for multi-agent systems via pinning leader-following approach

This paper addresses the group consensus problem of second-order nonlinear multi-agent systems through leader-following approach and pinning control. The network topology is assumed to be directed and weakly connected. The pinning consensus protocol is designed according to the agent property, that is, the inter-act agent and the intra-act agent. Some consensus criteria are proposed to guarantee that the agents asymptotically follow the virtual leader in each group, while agents in different groups behave independently. Numerical example is also provided to demonstrate the effectiveness of the theoretical analysis.     

Velocity observer design for the consensus in delayed robot networks

The consensus problem for networks of multiple agents consists in reaching an agreement between certain coordinates of interest using a distributed controller. It may be desirable that all the agents find a consensus at a given desired leader coordinate (Leader Follower Consensus Problem LFCP), or it may be only necessary that they agree at a certain coordinates value (Leaderless Consensus Problem LCP). Consensus has many practical applications in robot networks systems, where the interconnection of the agents may present variable time delays, hence rendering the stability analysis and control design more complex. Another problem that may arise is the possible lack of velocity measurements. In this work, a Proportional plus damping injection (P + d) controller together with a linear velocity observer is introduced. Our approach is able to solve both the LFCP and the LCP in networks of robots modeled as undirected weighted graphs with unknown asymmetric (bounded) variable time delays. Local (semi global) asymptotic stability is proven and simulation results are provided to test the performance of the proposed scheme.